Old-school film projectors could display at the distance/size because they used extremely bright xenon-filled bulbs inside the projector housing. All complexities aside, film was run in front of these extremely bright lights at 24 frames per second (for standard, 35mm theatrical film). Couple that with having expertly calibrated lenses, and there you go – a damn good picture on a screen.
Think of it like a shadow puppet. The better and brighter the light you shine on your hand, the “crisper” and darker the puppet image will be on a wall. Obviously this doesn’t take into account color grades and the like, but for ELI5, the answer is “the lights are bright as hell.”
Source: Old school film projectionist for many years.
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